BCN Spring 2016 Workshop: Number Theory & K-theory

The 1-type of Waldhausen $K$-theory as an abelian 2-group


Andrew Tonks


Abelian 2-groups are a straightforward generalisation of the notion of abelian group, related to the crossed modules of Whitehead and the Gr-categories of Grothendieck and  H. X. Sinh, which capture the information in the K-theory groups $K_0$ and $K_1$ together with the associated $k$-invariant.  In this talk will explain work in collaboration with F. Muro and M. Witte on how this can lead to an explicit calculation of the Waldhausen $K_1$ group, and to applications to universal determinant functors as introduced by Deligne.


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